
# First lets install the libraries
import tqdm
import requests
import numpy as np
import pandas as pd
import seaborn as sns
import networkx as nx
import plotly.express as px
from bs4 import BeautifulSoup
import matplotlib.pyplot as plt
import pandas_datareader.data as web

import warnings
warnings.filterwarnings('ignore')


from google.colab import drive
drive.mount('/content/drive')

Mounted at /content/drive


# Read the csv Data file using Pandas
stock_data = pd.read_csv('/content/drive/SP500_price_data_2010_to_2023.csv', index_col=[0])


stock_data


#create a heatmap visualization to display missing values in the stock_data DataFrame.
figure = plt.figure(figsize=(20, 10))
sns.heatmap(stock_data.T.isnull());


#clean the DataFrame stock_data by removing columns that contain any missing values
stock_data_cleaned = stock_data.dropna(axis=1)


# Plot the heatmap
figure = plt.figure(figsize=(20, 10))
sns.heatmap(stock_data_cleaned.T.isnull());


# Define the function to get year-wise S&P 500 data
def get_year_wise_snp_500_data(data, year):
    start_date = '{}-01-01'.format(year)
    end_date = '{}-12-31'.format(year)
    year_wise_data = data.loc[start_date:end_date]
    return year_wise_data

# Separate variable for each year containing the data specifically for that year.
snp_500_2010 = get_year_wise_snp_500_data(stock_data_cleaned, 2010)
snp_500_2011 = get_year_wise_snp_500_data(stock_data_cleaned, 2011)
snp_500_2012 = get_year_wise_snp_500_data(stock_data_cleaned, 2012)
snp_500_2013 = get_year_wise_snp_500_data(stock_data_cleaned, 2013)
snp_500_2014 = get_year_wise_snp_500_data(stock_data_cleaned, 2014)
snp_500_2015 = get_year_wise_snp_500_data(stock_data_cleaned, 2015)
snp_500_2016 = get_year_wise_snp_500_data(stock_data_cleaned, 2016)
snp_500_2017 = get_year_wise_snp_500_data(stock_data_cleaned, 2017)
snp_500_2018 = get_year_wise_snp_500_data(stock_data_cleaned, 2018)
snp_500_2019 = get_year_wise_snp_500_data(stock_data_cleaned, 2019)
snp_500_2020 = get_year_wise_snp_500_data(stock_data_cleaned, 2020)
snp_500_2021 = get_year_wise_snp_500_data(stock_data_cleaned, 2021)
snp_500_2022 = get_year_wise_snp_500_data(stock_data_cleaned, 2022)
snp_500_2023 = get_year_wise_snp_500_data(stock_data_cleaned, 2023)


#looking at the matrix for 2010
snp_500_2010


#looking at the matrix for 2010 shifted
snp_500_2010.shift(1)


# Calculating daily log returns by subtracting between two days with the help of shift function
log_returns_2010 = np.log(snp_500_2010.shift(1)) - np.log(snp_500_2010)
log_returns_2011 = np.log(snp_500_2011.shift(1)) - np.log(snp_500_2011)
log_returns_2012 = np.log(snp_500_2012.shift(1)) - np.log(snp_500_2012)
log_returns_2013 = np.log(snp_500_2013.shift(1)) - np.log(snp_500_2013)
log_returns_2014 = np.log(snp_500_2014.shift(1)) - np.log(snp_500_2014)
log_returns_2015 = np.log(snp_500_2015.shift(1)) - np.log(snp_500_2015)
log_returns_2016 = np.log(snp_500_2016.shift(1)) - np.log(snp_500_2016)
log_returns_2017 = np.log(snp_500_2017.shift(1)) - np.log(snp_500_2017)
log_returns_2018 = np.log(snp_500_2018.shift(1)) - np.log(snp_500_2018)
log_returns_2019 = np.log(snp_500_2019.shift(1)) - np.log(snp_500_2019)
log_returns_2020 = np.log(snp_500_2020.shift(1)) - np.log(snp_500_2020)
log_returns_2021 = np.log(snp_500_2021.shift(1)) - np.log(snp_500_2021)
log_returns_2022 = np.log(snp_500_2022.shift(1)) - np.log(snp_500_2022)
log_returns_2023 = np.log(snp_500_2023.shift(1)) - np.log(snp_500_2023)


# Visualise the Log returns for the year 2010
log_returns_2010


# Computing adjacency matrix:
return_correlation_2010 = log_returns_2010.corr()
return_correlation_2011 = log_returns_2011.corr()
return_correlation_2012 = log_returns_2012.corr()
return_correlation_2013 = log_returns_2013.corr()
return_correlation_2014 = log_returns_2014.corr()
return_correlation_2015 = log_returns_2015.corr()
return_correlation_2016 = log_returns_2016.corr()
return_correlation_2017 = log_returns_2017.corr()
return_correlation_2018 = log_returns_2018.corr()
return_correlation_2019 = log_returns_2019.corr()
return_correlation_2020 = log_returns_2020.corr()
return_correlation_2021 = log_returns_2021.corr()
return_correlation_2022 = log_returns_2022.corr()
return_correlation_2023 = log_returns_2023.corr()


#Visualise the corr Matrix for the year 2010
return_correlation_2010


figure, axes = plt.subplots(7, 2, figsize=(30, 30))

# Adding the heatmaps and setting titles with the corresponding year
sns.heatmap(return_correlation_2010, ax=axes[0, 0])
axes[0, 0].set_title('2010')

sns.heatmap(return_correlation_2011, ax=axes[0, 1])
axes[0, 1].set_title('2011')

sns.heatmap(return_correlation_2012, ax=axes[1, 0])
axes[1, 0].set_title('2012')

sns.heatmap(return_correlation_2013, ax=axes[1, 1])
axes[1, 1].set_title('2013')

sns.heatmap(return_correlation_2014, ax=axes[2, 0])
axes[2, 0].set_title('2014')

sns.heatmap(return_correlation_2015, ax=axes[2, 1])
axes[2, 1].set_title('2015')

sns.heatmap(return_correlation_2016, ax=axes[3, 0])
axes[3, 0].set_title('2016')

sns.heatmap(return_correlation_2017, ax=axes[3, 1])
axes[3, 1].set_title('2017')

sns.heatmap(return_correlation_2018, ax=axes[4, 0])
axes[4, 0].set_title('2018')

sns.heatmap(return_correlation_2019, ax=axes[4, 1])
axes[4, 1].set_title('2019')

sns.heatmap(return_correlation_2020, ax=axes[5, 0])
axes[5, 0].set_title('2020')

sns.heatmap(return_correlation_2021, ax=axes[5, 1])
axes[5, 1].set_title('2021')

sns.heatmap(return_correlation_2022, ax=axes[6, 0])
axes[6, 0].set_title('2022')

sns.heatmap(return_correlation_2023, ax=axes[6, 1])
axes[6, 1].set_title('2023')

# Adjusting layout for better display
plt.tight_layout()

# Display the plot
plt.show()


graph_2010 = nx.Graph(return_correlation_2010)


#Plot the Graph
figure = plt.figure(figsize=(24, 12))
nx.draw_networkx(graph_2010, with_labels=False,node_size=30,width=0.01)
plt.title('Network of S&P 500 Stock Market (2010)', fontsize=15)
plt.show()


# Convert the correlation coefficient
distance_2010 = np.sqrt(2 * (1 - return_correlation_2010))
distance_2011 = np.sqrt(2 * (1 - return_correlation_2011))
distance_2012 = np.sqrt(2 * (1 - return_correlation_2012))
distance_2013 = np.sqrt(2 * (1 - return_correlation_2013))
distance_2014 = np.sqrt(2 * (1 - return_correlation_2014))
distance_2015 = np.sqrt(2 * (1 - return_correlation_2015))
distance_2016 = np.sqrt(2 * (1 - return_correlation_2016))
distance_2017 = np.sqrt(2 * (1 - return_correlation_2017))
distance_2018 = np.sqrt(2 * (1 - return_correlation_2018))
distance_2019 = np.sqrt(2 * (1 - return_correlation_2019))
distance_2020 = np.sqrt(2 * (1 - return_correlation_2020))
distance_2021 = np.sqrt(2 * (1 - return_correlation_2021))
distance_2022 = np.sqrt(2 * (1 - return_correlation_2022))
distance_2023 = np.sqrt(2 * (1 - return_correlation_2023))


distance_2010.head(5)


# Transforms the distance matrices into Networks for every year
distance_2010_graph = nx.Graph(distance_2010)
distance_2011_graph = nx.Graph(distance_2011)
distance_2012_graph = nx.Graph(distance_2012)
distance_2013_graph = nx.Graph(distance_2013)
distance_2014_graph = nx.Graph(distance_2014)
distance_2015_graph = nx.Graph(distance_2015)
distance_2016_graph = nx.Graph(distance_2016)
distance_2017_graph = nx.Graph(distance_2017)
distance_2018_graph = nx.Graph(distance_2018)
distance_2019_graph = nx.Graph(distance_2019)
distance_2020_graph = nx.Graph(distance_2020)
distance_2021_graph = nx.Graph(distance_2021)
distance_2022_graph = nx.Graph(distance_2022)
distance_2023_graph = nx.Graph(distance_2023)


graph_2010_filtered = nx.minimum_spanning_tree(distance_2010_graph)
graph_2011_filtered = nx.minimum_spanning_tree(distance_2011_graph)
graph_2012_filtered = nx.minimum_spanning_tree(distance_2012_graph)
graph_2013_filtered = nx.minimum_spanning_tree(distance_2013_graph)
graph_2014_filtered = nx.minimum_spanning_tree(distance_2014_graph)
graph_2015_filtered = nx.minimum_spanning_tree(distance_2015_graph)
graph_2016_filtered = nx.minimum_spanning_tree(distance_2016_graph)
graph_2017_filtered = nx.minimum_spanning_tree(distance_2017_graph)
graph_2018_filtered = nx.minimum_spanning_tree(distance_2018_graph)
graph_2019_filtered = nx.minimum_spanning_tree(distance_2019_graph)
graph_2020_filtered = nx.minimum_spanning_tree(distance_2020_graph)
graph_2021_filtered = nx.minimum_spanning_tree(distance_2021_graph)
graph_2022_filtered = nx.minimum_spanning_tree(distance_2022_graph)
graph_2023_filtered = nx.minimum_spanning_tree(distance_2023_graph)


figure, axes = plt.subplots(14, 1, figsize=(24, 120))

nx.draw_networkx(graph_2011_filtered, with_labels=False, ax=axes[1],node_size=200)
axes[1].set_title('MST Based Network Graph for 2011', fontsize=16)

nx.draw_networkx(graph_2012_filtered, with_labels=False, ax=axes[2],node_size=200)
axes[2].set_title('MST Based Network Graph for 2012', fontsize=16)

nx.draw_networkx(graph_2013_filtered, with_labels=False, ax=axes[3],node_size=200)
axes[3].set_title('MST Based Network Graph for 2013', fontsize=16)

nx.draw_networkx(graph_2014_filtered, with_labels=False, ax=axes[4],node_size=200)
axes[4].set_title('MST Based Network Graph for 2014', fontsize=16)

nx.draw_networkx(graph_2015_filtered, with_labels=False, ax=axes[5],node_size=200)
axes[5].set_title('MST Based Network Graph for 2015', fontsize=16)

nx.draw_networkx(graph_2016_filtered, with_labels=False, ax=axes[6],node_size=200)
axes[6].set_title('MST Based Network Graph for 2016', fontsize=16)

nx.draw_networkx(graph_2017_filtered, with_labels=False, ax=axes[7],node_size=200)
axes[7].set_title('MST Based Network Graph for 2017', fontsize=16)

nx.draw_networkx(graph_2018_filtered, with_labels=False, ax=axes[8],node_size=200)
axes[8].set_title('MST Based Network Graph for 2018', fontsize=16)

nx.draw_networkx(graph_2019_filtered, with_labels=False, ax=axes[9],node_size=200)
axes[9].set_title('MST Based Network Graph for 2019', fontsize=16)

nx.draw_networkx(graph_2020_filtered, with_labels=False, ax=axes[10],node_size=200)
axes[10].set_title('MST Based Network Graph for 2020', fontsize=16)

nx.draw_networkx(graph_2021_filtered, with_labels=False, ax=axes[11],node_size=200)
axes[11].set_title('MST Based Network Graph for 2021', fontsize=16)

nx.draw_networkx(graph_2022_filtered, with_labels=False, ax=axes[12],node_size=200)
axes[12].set_title('MST Based Network Graph for 2022', fontsize=16)

nx.draw_networkx(graph_2023_filtered, with_labels=False, ax=axes[13],node_size=200)
axes[13].set_title('MST Based Network Graph for 2023', fontsize=16)

plt.tight_layout()
plt.show()


#Create empty lists
average_degree_connectivity = []
average_shortest_path_length = []
year = [2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019, 2020, 2021, 2022,2023]

# Create a loop Through Each Year’s Graph:
for graph in [graph_2010_filtered, graph_2011_filtered, graph_2012_filtered, graph_2013_filtered, graph_2014_filtered, graph_2015_filtered,
             graph_2016_filtered, graph_2017_filtered, graph_2018_filtered, graph_2019_filtered, graph_2020_filtered, graph_2021_filtered, graph_2022_filtered,graph_2023_filtered]:

    # nx.average_shortest_path_length(graph) function from the NetworkX library is used to calculate the average shortest path length
    average_shortest_path_length.append(nx.average_shortest_path_length(graph))


# Plot the
figure = plt.figure(figsize=(22, 8))
sns.lineplot(x='year', y='average_shortest_path_length',
             data=pd.DataFrame({'year': year, 'average_shortest_path_length': average_shortest_path_length}));


# Calculate the log returns of the stocks over time 2010 to 2023
log_returns_2010_till_2023 = np.log(stock_data_cleaned.shift(1)) - np.log(stock_data_cleaned)
# Calculate the correlation matrix of the log returns 2010 to 2023
return_correlation_2010_till_2023 = log_returns_2010_till_2023.corr()


# Plot the correlation matrix as heatmap
figure = plt.figure(figsize=(24, 8))
sns.heatmap(return_correlation_2010_till_2023);


distance_2010_till_2023 = np.sqrt(2 * (1 - return_correlation_2010_till_2023))


distance_2010_till_2023_graph = nx.Graph(distance_2010_till_2023)
distance_2010_till_2023_graph_filtered = nx.minimum_spanning_tree(distance_2010_till_2023_graph)


# Get the number of nodes in the graph
num_nodes = distance_2010_till_2023_graph_filtered.number_of_nodes()
print("Number of nodes:", num_nodes)

# Get the number of edges in the graph
num_edges = distance_2010_till_2023_graph_filtered.number_of_edges()
print("Number of edges:", num_edges)

# Check if the graph is connected
is_connected = nx.is_connected(distance_2010_till_2023_graph_filtered)
print("Is the graph connected?", is_connected)

Number of nodes: 420
Number of edges: 419
Is the graph connected? True


figure = plt.figure(figsize=(24, 12))
# Lets visualise the plot using the nx.draw_kamada_kawai function from the NetworkX library in order to make the visualization more interpretable.
nx.draw_kamada_kawai(distance_2010_till_2023_graph_filtered, with_labels=False,node_size=200)

# Display the plot
plt.title('MST Graph of S&P 500 Stock Market (2010-2023)', fontsize=20)
plt.show()


degree_centrality = nx.degree_centrality(distance_2010_till_2023_graph_filtered)


# Create the Bar chart showing the Degree Centralty among stocks
keys = []
values = []

for key, value in degree_centrality.items():
    keys.append(key)
    values.append(value)

dc_data = pd.DataFrame({'stocks': keys, 'degree_centrality': values}).sort_values('degree_centrality', ascending=False)
px.bar(data_frame=dc_data, x='stocks', y='degree_centrality', template='plotly_dark')


from IPython.display import Image, display
# Display the image as a PNG for the HTML
display(Image(filename='newplot.png'))


closeness_centrality = nx.closeness_centrality(distance_2010_till_2023_graph_filtered)


keys = []
values = []

for key, value in closeness_centrality.items():
    keys.append(key)
    values.append(value)

cc_data = pd.DataFrame({'stocks': keys, 'closeness_centrality': values}).sort_values('closeness_centrality',
                                                                                       ascending=False)
px.bar(data_frame=cc_data, x='stocks', y='closeness_centrality', template='plotly_dark')


from IPython.display import Image, display
# Display the image as a PNG for the HTML
display(Image(filename='newplot (1).png'))


betweenness_centrality = nx.betweenness_centrality(distance_2010_till_2023_graph_filtered)


keys = []
values = []

for key, value in betweenness_centrality.items():
    keys.append(key)
    values.append(value)

bc_data = pd.DataFrame({'stocks': keys, 'betweenness_centrality': values}).sort_values('betweenness_centrality',
                                                                                       ascending=False)
px.bar(data_frame=bc_data, x='stocks', y='betweenness_centrality', template='plotly_dark')


from IPython.display import Image, display
# Display the image as a PNG for the HTML
display(Image(filename='newplot (2).png'))


eigenvector_centrality=nx.eigenvector_centrality_numpy(distance_2010_till_2023_graph_filtered)


keys = []
values = []

for key, value in eigenvector_centrality.items():
    keys.append(key)
    values.append(value)

bc_data = pd.DataFrame({'stocks': keys, 'eigenvector_centrality': values}).sort_values('eigenvector_centrality',ascending=False)
px.bar(data_frame=bc_data, x='stocks', y='eigenvector_centrality', template='plotly_dark')


from IPython.display import Image, display
# Display the image as a PNG for the HTML
display(Image(filename='/content/drive/newplot (3).png'))


# Distance on Degree Criterion

# Initialize dictionary to store shortest path lengths to the node with the highest degree centrality
distance_degree_criteria = {}

# Identify the node with the largest degree centrality (most connections)
node_with_largest_degree_centrality = max(dict(degree_centrality), key=dict(degree_centrality).get)

# Calculate and store the shortest path length from each node to the node with the largest degree centrality
for node in distance_2010_till_2023_graph_filtered.nodes():
    distance_degree_criteria[node] = nx.shortest_path_length(distance_2010_till_2023_graph_filtered, node, node_with_largest_degree_centrality)


# Distance on Correlation Criterion

# Initialize dictionaries to store shortest path lengths and sum of correlations
distance_correlation_criteria = {}
sum_correlation = {}

# Calculate the sum of correlations for each node with its neighbors
for node in distance_2010_till_2023_graph_filtered.nodes():
    neighbors = nx.neighbors(distance_2010_till_2023_graph_filtered, node)
    sum_correlation[node] = sum(return_correlation_2010_till_2023.loc[node, neighbor] for neighbor in neighbors)

# Identify the node with the highest sum of correlations with its neighbors
node_with_highest_correlation = max(sum_correlation, key=sum_correlation.get)

# Calculate and store the shortest path length from each node to the node with the highest correlation
for node in distance_2010_till_2023_graph_filtered.nodes():
    distance_correlation_criteria[node] = nx.shortest_path_length(distance_2010_till_2023_graph_filtered, node, node_with_highest_correlation)


# Distance on Distance Criterion

# Initialize dictionaries to store shortest path lengths and mean distances
distance_distance_criteria = {}
mean_distance = {}

# Calculate the mean shortest path distance from each node to all other nodes
for node in distance_2010_till_2023_graph_filtered.nodes():
    nodes = list(distance_2010_till_2023_graph_filtered.nodes())
    nodes.remove(node)
    distance_distance = [nx.shortest_path_length(distance_2010_till_2023_graph_filtered, node, ns) for ns in nodes]
    mean_distance[node] = np.mean(distance_distance)

# Identify the node with the minimum mean distance to all other nodes
node_with_minimum_mean_distance = min(mean_distance, key=mean_distance.get)

# Calculate and store the shortest path length from each node to the node with the minimum mean distance
for node in distance_2010_till_2023_graph_filtered.nodes():
    distance_distance_criteria[node] = nx.shortest_path_length(distance_2010_till_2023_graph_filtered, node, node_with_minimum_mean_distance)


# Store the results in a DataFrame

# Create a DataFrame from the degree centrality dictionary
node_stats = pd.DataFrame.from_dict(dict(degree_centrality), orient='index')

# Add betweenness centrality to the DataFrame
node_stats.columns = ['degree_centrality']

# Add the distance criteria results to the DataFrame
node_stats['betweenness_centrality'] = pd.Series(betweenness_centrality)
node_stats['distance_degree_criteria'] = pd.Series(distance_degree_criteria)
node_stats['distance_correlation_criteria'] = pd.Series(distance_correlation_criteria)
node_stats['distance_distance_criteria'] = pd.Series(distance_distance_criteria)

# Calculate the average of the distance criteria and store it in the DataFrame
node_stats['average_distance'] = (
    node_stats['distance_degree_criteria'] + node_stats['distance_correlation_criteria'] + node_stats['distance_distance_criteria']) / 3


# Add closeness centrality and eigenvector centrality to the DataFrame
node_stats['closeness_centrality'] = pd.Series(closeness_centrality)
node_stats['eigenvector_centrality'] = pd.Series(eigenvector_centrality) # Add this line to include eigenvector centrality


# Centrality Normalization

# Normalize degree centrality
node_stats['degree_centrality_norm'] = (
    node_stats['degree_centrality'] - node_stats['degree_centrality'].min()) / (node_stats['degree_centrality'].max() - node_stats['degree_centrality'].min())

# Normalize closeness centrality
node_stats['closeness_centrality_norm'] = (
    node_stats['closeness_centrality'] - node_stats['closeness_centrality'].min()) / (node_stats['closeness_centrality'].max() - node_stats['closeness_centrality'].min())

# Normalize betweenness centrality
node_stats['betweenness_centrality_norm'] = (
    node_stats['betweenness_centrality'] - node_stats['betweenness_centrality'].min()) / (node_stats['betweenness_centrality'].max() - node_stats['betweenness_centrality'].min())

# Normalize eigenvector centrality
node_stats['eigenvector_centrality_norm'] = (
    node_stats['eigenvector_centrality'] - node_stats['eigenvector_centrality'].min()) / (node_stats['eigenvector_centrality'].max() - node_stats['eigenvector_centrality'].min())

# Combined Centrality Score

# Calculate the combined centrality score as the average of all normalized centralities
node_stats['combined_centrality'] = (node_stats['degree_centrality_norm'] +
                                      node_stats['closeness_centrality_norm'] +
                                      node_stats['betweenness_centrality_norm'] +
                                      node_stats['eigenvector_centrality_norm']) / 4


# Final Combined Score (Weighted)
final_weighted_score = 0.7 * node_stats['combined_centrality'] + 0.3 * (1 / node_stats['average_distance'])
node_stats['final_score'] = final_weighted_score

# Sort based on the final score
node_stats_sorted = node_stats.sort_values(by='final_score', ascending=False)


# Select the top 15 central stocks
central_stocks = node_stats_sorted.head(15)
central_portfolio = [stock for stock in central_stocks.index.values]

# Select the last 15 peripheral stocks
peripheral_stocks = node_stats_sorted.tail(15)
peripheral_portfolio = [stock for stock in peripheral_stocks.index.values]


color = []

for node in distance_2010_till_2023_graph_filtered:
    if node in central_portfolio:
        color.append('red')

    elif node in peripheral_portfolio:
        color.append('green')

    else:
        color.append('blue')

# Plot the graph using the Kamada-Kawai layout
figure, ax = plt.subplots(figsize=(24, 12))
nx.draw_kamada_kawai(distance_2010_till_2023_graph_filtered, with_labels=False, node_color=color, ax=ax,node_size=100)

# Create a legend directly
ax.legend(handles=[plt.Line2D([0], [0], marker='o', color='w', markerfacecolor='red', markersize=10, label='Central Portfolio'),
                   plt.Line2D([0], [0], marker='o', color='w', markerfacecolor='green', markersize=10, label='Peripheral Portfolio'),
                   plt.Line2D([0], [0], marker='o', color='w', markerfacecolor='blue', markersize=10, label='S&P 500')],
          loc='upper left')

# Add a title to the plot
ax.set_title('Network Graph Visualization of Central and Peripheral Stocks (2010-2023)', fontsize=16)

# Display the plot
plt.show()


#Reading data for 2024 S&P 500 stocks:
stock_data_2024 = pd.read_csv('/content/drive/SP500_price_data_2024_till_August.csv', index_col=[0])


stock_data_2024


# Get the S&P500 historical data for the year 2024 from pandas_datareader
snp_500_2024 = web.DataReader(['sp500'], 'fred', start='2024-01-01', end='2024-08-22')
snp_500_2024


# Drop columns with any NA values
stock_data_2024 = stock_data_2024.dropna(axis=1)
snp_500_2024 = snp_500_2024.dropna()

# Convert indices to datetime to ensuring proper alignment by date
stock_data_2024.index = pd.to_datetime(stock_data_2024.index)
snp_500_2024.index = pd.to_datetime(snp_500_2024.index)

# Find common dates between the stock data and the S&P 500 data
common_dates = stock_data_2024.index.intersection(snp_500_2024.index)

# Select from both dataframes to include only the common dates
stock_data_2024 = stock_data_2024.loc[common_dates]
snp_500_2024 = snp_500_2024.loc[common_dates]


snp_500_2024.shape

(162, 1)


stock_data_2024.shape

(162, 475)


stock_data_2024


# Initial investment amount
amount = 10000


# Creating an empty DataFrame to store the values of stocks in the central portfolio
central_portfolio_value = pd.DataFrame()
for stock in central_portfolio:
    central_portfolio_value[stock] = stock_data_2024[stock]

portfolio_unit = central_portfolio_value.sum(axis=1)[0] # calculates the sum of the first row to found the initial value of the portfolio.
share = amount / portfolio_unit # Find the shares by dividing the initial investment by the initial portfolio value
central_portfolio_value = central_portfolio_value.sum(axis=1) * share # Calculate the value of the central portfolio over time

# Similar is the process for the Peripheral Portfolio Value Calculation

peripheral_portfolio_value = pd.DataFrame()
for stock in peripheral_portfolio:
    peripheral_portfolio_value[stock] = stock_data_2024[stock]

portfolio_unit = peripheral_portfolio_value.sum(axis=1)[0]
share = amount / portfolio_unit
peripheral_portfolio_value = peripheral_portfolio_value.sum(axis=1) * share


# Scale the S&P 500 index values to reflect an initial investment amount
snp_500_2024_value = snp_500_2024 * (amount / snp_500_2024.iloc[0])


all_portfolios = snp_500_2024_value
all_portfolios['central_portfolio'] = central_portfolio_value.values
all_portfolios['peripheral_portfolio'] = peripheral_portfolio_value.values


all_portfolios.tail()


figure, ax = plt.subplots(figsize=(16, 8))

# Plot S&P 500 values
snp_500_line = ax.plot(all_portfolios['sp500'], label='S&P 500')

# Plot Central Portfolio values
central_portfolio_line = ax.plot(all_portfolios['central_portfolio'], label= 'Central Portfolio', color= 'red')

# Plot Peripheral Portfolio values
peripheral_portfolio_line = ax.plot(all_portfolios['peripheral_portfolio'], label= 'Peripheral Portfolio', color= 'green')

ax.legend(loc='upper left')

# Title to the plot
ax.set_title('Portfolio Performance Comparison')

# Adding a title to the Y-axis
ax.set_ylabel('Investment Value ')

plt.show()

	MMM	AOS	ABT	ABBV	ABMD	ACN	ATVI	ADM	ADBE	ADP	...	WYNN	XEL	XYL	YUM	ZBRA	ZBH	ZION	ZTS	CEG	OGN
Date
2010-01-04	69.414719	7.435000	26.129908	NaN	8.74	42.070000	NaN	31.469999	37.090000	37.603161	...	63.959999	21.080000	NaN	25.226456	28.670000	58.271847	13.330000	NaN	NaN	NaN
2010-01-05	68.979935	7.340000	25.918797	NaN	8.53	42.330002	NaN	31.639999	37.700001	37.401230	...	67.849998	20.830000	NaN	25.140186	28.620001	60.116505	13.800000	NaN	NaN	NaN
2010-01-06	69.958191	7.343333	26.062737	NaN	8.40	42.779999	NaN	31.559999	37.619999	37.313435	...	66.959999	20.870001	NaN	24.960461	28.400000	60.097088	15.000000	NaN	NaN	NaN
2010-01-07	70.008362	7.365000	26.278646	NaN	8.40	42.740002	NaN	31.230000	36.889999	37.295876	...	68.389999	20.780001	NaN	24.953272	27.690001	61.475727	16.680000	NaN	NaN	NaN
2010-01-08	70.501671	7.473333	26.412991	NaN	8.23	42.570000	NaN	30.840000	36.689999	37.243195	...	67.900002	20.790001	NaN	24.960461	27.600000	60.184467	16.410000	NaN	NaN	NaN
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
2023-12-22	88.904678	81.730003	109.029999	154.940002	NaN	354.450012	NaN	71.459999	598.750000	230.970001	...	90.419998	62.060001	112.639999	130.000000	269.410004	120.559998	44.000000	194.979996	115.330002	13.91
2023-12-26	90.392975	81.849998	109.230003	154.619995	NaN	353.429993	NaN	72.389999	598.260010	232.539993	...	91.000000	62.250000	113.620003	130.259995	275.500000	121.419998	44.880001	195.500000	117.570000	14.13
2023-12-27	90.919731	82.160004	109.790001	154.880005	NaN	353.820007	NaN	72.169998	596.080017	231.610001	...	90.629997	61.540001	114.379997	130.839996	275.790009	121.129997	44.509998	196.899994	117.419998	14.36
2023-12-28	91.714050	82.239998	110.400002	154.750000	NaN	351.589996	NaN	72.269997	595.520020	232.490005	...	91.760002	61.889999	114.320000	130.520004	275.350006	121.629997	44.660000	197.160004	117.110001	14.48
2023-12-29	91.404678	82.440002	110.070000	154.970001	NaN	350.910004	NaN	72.220001	596.599976	232.970001	...	91.110001	61.910000	114.360001	130.660004	273.329987	121.699997	43.869999	197.369995	116.889999	14.42

	MMM	AOS	ABT	ACN	ADM	ADBE	ADP	AAP	AES	AFL	...	WY	WHR	WMB	WTW	WYNN	XEL	YUM	ZBRA	ZBH	ZION
Date
2010-01-04	69.414719	7.435000	26.129908	42.070000	31.469999	37.090000	37.603161	40.380001	13.67	23.785000	...	44.279999	81.949997	17.616472	70.913910	63.959999	21.080000	25.226456	28.670000	58.271847	13.330000
2010-01-05	68.979935	7.340000	25.918797	42.330002	31.639999	37.700001	37.401230	40.139999	13.53	24.475000	...	45.220001	81.779999	17.836576	70.754967	67.849998	20.830000	25.140186	28.620001	60.116505	13.800000
2010-01-06	69.958191	7.343333	26.062737	42.779999	31.559999	37.619999	37.313435	40.490002	13.39	24.690001	...	44.720001	81.059998	18.415367	71.894043	66.959999	20.870001	24.960461	28.400000	60.097088	15.000000
2010-01-07	70.008362	7.365000	26.278646	42.740002	31.230000	36.889999	37.295876	40.480000	13.40	24.955000	...	44.520000	82.800003	18.284937	71.682121	68.389999	20.780001	24.953272	27.690001	61.475727	16.680000
2010-01-08	70.501671	7.473333	26.412991	42.570000	30.840000	36.689999	37.243195	40.639999	13.78	24.705000	...	44.110001	84.559998	18.431671	71.602646	67.900002	20.790001	24.960461	27.600000	60.184467	16.410000
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
2010-12-27	72.750839	9.722500	22.732924	48.250000	30.090000	30.950001	40.886742	66.419998	12.17	28.485001	...	18.709999	90.330002	20.078377	91.072845	102.120003	23.459999	35.600288	38.419998	52.864079	24.100000
2010-12-28	72.525085	9.637500	22.737722	47.980000	29.780001	30.920000	40.851624	66.250000	12.09	28.445000	...	18.840000	90.309998	20.070225	91.682121	101.690002	23.520000	35.391804	38.250000	52.582523	24.459999
2010-12-29	72.541809	9.680000	22.752115	48.619999	29.750000	30.969999	40.798946	66.449997	12.15	28.350000	...	19.000000	90.000000	20.176201	91.629143	102.610001	23.500000	35.657799	38.439999	52.398060	24.270000
2010-12-30	72.357857	9.650000	22.824085	48.419998	29.900000	30.570000	40.763828	66.720001	12.20	28.045000	...	18.950001	89.820000	20.102833	91.814568	101.709999	23.549999	35.449318	38.299999	52.330097	24.270000
2010-12-31	72.157188	9.520000	22.987219	48.490002	30.080000	30.780001	40.632133	66.150002	12.18	28.215000	...	18.930000	88.830002	20.151745	91.735100	103.839996	23.549999	35.262402	37.990002	52.116505	24.230000

	MMM	AOS	ABT	ACN	ADM	ADBE	ADP	AAP	AES	AFL	...	WY	WHR	WMB	WTW	WYNN	XEL	YUM	ZBRA	ZBH	ZION
Date
2010-01-04	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	...	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN
2010-01-05	69.414719	7.435000	26.129908	42.070000	31.469999	37.090000	37.603161	40.380001	13.67	23.785000	...	44.279999	81.949997	17.616472	70.913910	63.959999	21.080000	25.226456	28.670000	58.271847	13.330000
2010-01-06	68.979935	7.340000	25.918797	42.330002	31.639999	37.700001	37.401230	40.139999	13.53	24.475000	...	45.220001	81.779999	17.836576	70.754967	67.849998	20.830000	25.140186	28.620001	60.116505	13.800000
2010-01-07	69.958191	7.343333	26.062737	42.779999	31.559999	37.619999	37.313435	40.490002	13.39	24.690001	...	44.720001	81.059998	18.415367	71.894043	66.959999	20.870001	24.960461	28.400000	60.097088	15.000000
2010-01-08	70.008362	7.365000	26.278646	42.740002	31.230000	36.889999	37.295876	40.480000	13.40	24.955000	...	44.520000	82.800003	18.284937	71.682121	68.389999	20.780001	24.953272	27.690001	61.475727	16.680000
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
2010-12-27	72.299332	9.717500	22.939238	48.340000	30.209999	30.850000	40.842846	66.570000	12.23	28.555000	...	18.559999	89.860001	20.070225	91.390732	103.000000	23.469999	35.700935	38.490002	52.834949	23.740000
2010-12-28	72.750839	9.722500	22.732924	48.250000	30.090000	30.950001	40.886742	66.419998	12.17	28.485001	...	18.709999	90.330002	20.078377	91.072845	102.120003	23.459999	35.600288	38.419998	52.864079	24.100000
2010-12-29	72.525085	9.637500	22.737722	47.980000	29.780001	30.920000	40.851624	66.250000	12.09	28.445000	...	18.840000	90.309998	20.070225	91.682121	101.690002	23.520000	35.391804	38.250000	52.582523	24.459999
2010-12-30	72.541809	9.680000	22.752115	48.619999	29.750000	30.969999	40.798946	66.449997	12.15	28.350000	...	19.000000	90.000000	20.176201	91.629143	102.610001	23.500000	35.657799	38.439999	52.398060	24.270000
2010-12-31	72.357857	9.650000	22.824085	48.419998	29.900000	30.570000	40.763828	66.720001	12.20	28.045000	...	18.950001	89.820000	20.102833	91.814568	101.709999	23.549999	35.449318	38.299999	52.330097	24.270000

	MMM	AOS	ABT	ACN	ADM	ADBE	ADP	AAP	AES	AFL	...	WY	WHR	WMB	WTW	WYNN	XEL	YUM	ZBRA	ZBH	ZION
Date
2010-01-04	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	...	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN
2010-01-05	0.006283	0.012860	0.008112	-0.006161	-0.005387	-0.016313	0.005385	0.005961	0.010294	-0.028597	...	-0.021006	0.002077	-0.012417	0.002244	-0.059041	0.011930	0.003426	0.001745	-0.031165	-0.034651
2010-01-06	-0.014082	-0.000454	-0.005538	-0.010575	0.002532	0.002124	0.002350	-0.008682	0.010401	-0.008746	...	0.011119	0.008843	-0.031934	-0.015971	0.013204	-0.001919	0.007175	0.007717	0.000323	-0.083382
2010-01-07	-0.000717	-0.002946	-0.008250	0.000935	0.010511	0.019595	0.000471	0.000247	-0.000746	-0.010676	...	0.004482	-0.021239	0.007108	0.002952	-0.021131	0.004322	0.000288	0.025318	-0.022681	-0.106160
2010-01-08	-0.007022	-0.014602	-0.005099	0.003986	0.012567	0.005436	0.001414	-0.003945	-0.027964	0.010069	...	0.009252	-0.021033	-0.007993	0.001109	0.007191	-0.000481	-0.000288	0.003256	0.021228	0.016320
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
2010-12-27	-0.006226	-0.000514	0.009035	0.001864	0.003980	-0.003236	-0.001074	0.002256	0.004918	0.002454	...	-0.008049	-0.005217	-0.000406	0.003484	0.008580	0.000426	0.002823	0.001820	-0.000551	-0.015050
2010-12-28	0.003108	0.008781	-0.000211	0.005612	0.010356	0.000970	0.000859	0.002563	0.006595	0.001405	...	-0.006924	0.000221	0.000406	-0.006668	0.004220	-0.002554	0.005873	0.004435	0.005340	-0.014827
2010-12-29	-0.000231	-0.004400	-0.000633	-0.013251	0.001008	-0.001616	0.001290	-0.003014	-0.004950	0.003345	...	-0.008457	0.003438	-0.005266	0.000578	-0.009006	0.000851	-0.007488	-0.004955	0.003514	0.007798
2010-12-30	0.002539	0.003104	-0.003158	0.004122	-0.005029	0.013000	0.000861	-0.004055	-0.004107	0.010817	...	0.002635	0.002002	0.003643	-0.002022	0.008810	-0.002125	0.005864	0.003649	0.001298	0.000000
2010-12-31	0.002777	0.013563	-0.007122	-0.001445	-0.006002	-0.006846	0.003236	0.008580	0.001641	-0.006043	...	0.001056	0.011083	-0.002430	0.000866	-0.020726	0.000000	0.005287	0.008127	0.004090	0.001650

	MMM	AOS	ABT	ACN	ADM	ADBE	ADP	AAP	AES	AFL	...	WY	WHR	WMB	WTW	WYNN	XEL	YUM	ZBRA	ZBH	ZION
MMM	1.000000	0.593484	0.483927	0.486274	0.432142	0.334670	0.676420	0.253205	0.583607	0.686239	...	0.136096	0.622998	0.621104	0.524046	0.541869	0.593247	0.588807	0.525908	0.569811	0.485266
AOS	0.593484	1.000000	0.399469	0.346007	0.323026	0.305744	0.527425	0.288655	0.524470	0.591544	...	0.191281	0.529962	0.558584	0.439802	0.457564	0.467970	0.509763	0.526935	0.388246	0.455234
ABT	0.483927	0.399469	1.000000	0.445754	0.442076	0.290392	0.495372	0.156493	0.487559	0.532127	...	0.121300	0.450807	0.499627	0.415275	0.403185	0.560456	0.451432	0.411371	0.401872	0.416013
ACN	0.486274	0.346007	0.445754	1.000000	0.360045	0.255378	0.537841	0.183239	0.457032	0.521398	...	0.177261	0.472019	0.454769	0.499239	0.442191	0.430872	0.510435	0.438993	0.428124	0.394382
ADM	0.432142	0.323026	0.442076	0.360045	1.000000	0.210313	0.506797	0.284246	0.428716	0.489294	...	0.061361	0.387251	0.458206	0.406431	0.350003	0.480415	0.508323	0.442256	0.344112	0.308510
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
XEL	0.593247	0.467970	0.560456	0.430872	0.480415	0.357840	0.650324	0.281257	0.613973	0.641188	...	0.143083	0.515557	0.609604	0.462807	0.488771	1.000000	0.603322	0.524355	0.453095	0.436663
YUM	0.588807	0.509763	0.451432	0.510435	0.508323	0.345217	0.695521	0.423742	0.611902	0.703039	...	0.083662	0.557554	0.590081	0.480745	0.632180	0.603322	1.000000	0.573824	0.438971	0.489627
ZBRA	0.525908	0.526935	0.411371	0.438993	0.442256	0.386711	0.598238	0.338250	0.536078	0.586118	...	0.100419	0.516997	0.587588	0.430601	0.499715	0.524355	0.573824	1.000000	0.469623	0.435329
ZBH	0.569811	0.388246	0.401872	0.428124	0.344112	0.297990	0.558904	0.219691	0.423741	0.528562	...	0.193002	0.510361	0.465346	0.455785	0.451811	0.453095	0.438971	0.469623	1.000000	0.387305
ZION	0.485266	0.455234	0.416013	0.394382	0.308510	0.374793	0.505663	0.290643	0.528292	0.618436	...	0.350160	0.538962	0.516113	0.417525	0.468152	0.436663	0.489627	0.435329	0.387305	1.000000

	MMM	AOS	ABT	ACN	ADM	ADBE	ADP	AAP	AES	AFL	...	WY	WHR	WMB	WTW	WYNN	XEL	YUM	ZBRA	ZBH	ZION
MMM	0.000000	0.901683	1.015946	1.013633	1.065700	1.153542	0.804463	1.222126	0.912571	0.792162	...	1.314461	0.868334	0.870513	0.975658	0.957215	0.901946	0.906855	0.973747	0.927566	1.014627
AOS	0.901683	0.000000	1.095930	1.143672	1.163593	1.178351	0.972188	1.192765	0.975223	0.903831	...	1.271785	0.969575	0.939591	1.058488	1.041572	1.031533	0.990189	0.972692	1.106123	1.043806
ABT	1.015946	1.095930	0.000000	1.052850	1.056337	1.191308	1.004617	1.298851	1.012364	0.967339	...	1.325669	1.048039	1.000373	1.081411	1.092534	0.937597	1.047442	1.085015	1.093735	1.080728
ACN	1.013633	1.143672	1.052850	0.000000	1.131331	1.220346	0.961415	1.278093	1.042082	0.978368	...	1.282762	1.027600	1.044252	1.000761	1.056228	1.066891	0.989510	1.059252	1.069464	1.100562
ADM	1.065700	1.163593	1.056337	1.131331	0.000000	1.256732	0.993180	1.196457	1.068909	1.010650	...	1.370138	1.107022	1.040956	1.089559	1.140173	1.019397	0.991642	1.056167	1.145328	1.176001

	MMM	AOS	ABT	ABBV	ABMD	ACN	ATVI	ADM	ADBE	ADP	...	WYNN	XEL	XYL	YUM	ZBRA	ZBH	ZION	ZTS	CEG	OGN
Date
2024-01-02	91.973244	81.440002	109.849998	159.820007	NaN	346.920013	NaN	72.760002	580.070007	233.419998	...	94.599998	63.470001	113.669998	129.029999	267.980011	121.389999	44.139999	196.570007	115.250000	14.710000
2024-01-03	90.125420	78.709999	109.519997	160.460007	NaN	337.920013	NaN	73.129997	571.789978	232.509995	...	94.029999	63.580002	111.559998	129.100006	252.520004	120.470001	42.000000	192.929993	115.849998	14.630000
2024-01-04	90.443146	79.379997	110.980003	161.460007	NaN	337.089996	NaN	71.750000	567.049988	233.660004	...	94.209999	63.730000	112.330002	128.690002	252.970001	120.199997	42.639999	194.039993	115.360001	13.780000
2024-01-05	90.794312	79.040001	110.800003	162.139999	NaN	336.619995	NaN	70.809998	564.599976	235.210007	...	95.650002	63.730000	112.150002	128.339996	252.690002	119.980003	44.049999	194.850006	116.239998	14.410000
2024-01-08	91.020065	79.269997	112.400002	161.429993	NaN	340.350006	NaN	71.059998	580.549988	236.759995	...	97.050003	63.580002	112.849998	128.639999	261.089996	121.970001	44.540001	196.149994	117.029999	16.299999
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
2024-08-16	127.050003	79.650002	111.000000	193.899994	NaN	326.920013	NaN	59.090000	553.460022	264.089996	...	76.290001	59.980000	132.800003	137.399994	344.140015	110.650002	46.590000	183.710007	189.979996	20.350000
2024-08-19	127.080002	80.699997	111.900002	196.869995	NaN	329.440002	NaN	59.680000	563.119995	264.649994	...	76.599998	60.150002	134.380005	136.690002	347.019989	111.769997	47.000000	184.479996	192.779999	20.959999
2024-08-20	127.699997	80.800003	110.769997	196.149994	NaN	330.369995	NaN	59.009998	562.250000	264.540009	...	76.019997	59.990002	134.149994	136.949997	344.850006	111.639999	46.360001	183.600006	190.720001	20.799999
2024-08-21	129.229996	81.879997	111.389999	196.529999	NaN	333.600006	NaN	59.220001	565.789978	267.850006	...	77.360001	59.959999	135.800003	137.750000	345.000000	112.129997	47.070000	182.899994	196.740005	21.030001
2024-08-22	128.600006	81.129997	112.099998	196.369995	NaN	330.570007	NaN	59.250000	557.440002	269.380005	...	77.089996	59.919998	135.419998	136.759995	342.160004	113.419998	47.680000	182.169998	194.949997	20.889999

	sp500
DATE
2024-01-01	NaN
2024-01-02	4742.83
2024-01-03	4704.81
2024-01-04	4688.68
2024-01-05	4697.24
...	...
2024-08-16	5554.25
2024-08-19	5608.25
2024-08-20	5597.12
2024-08-21	5620.85
2024-08-22	5570.64

	sp500	central_portfolio	peripheral_portfolio
2024-08-16	11710.835092	10960.916494	10045.654823
2024-08-19	11824.691165	11031.035246	10190.822537
2024-08-20	11801.224164	10988.220295	10220.127797
2024-08-21	11851.257582	11069.043105	10223.182570
2024-08-22	11745.392519	11048.649683	10161.574208

Stock Market Analysis with the use of Networks¶

Approach¶

Loading the Libraries¶

Load the data¶

Visualize the Price Data for all the S&P 500 of 14 years till 29 December2023¶

Missing Data¶

The null values are removed - the data is clean and the plot below helps in finding that there are no missing values anymore.¶

Getting Yearwise Data¶

Computing the Daily Log Returns¶

Computing the Correlation of Returns¶

Observations:¶

Plot the heat Maps¶

Observations and Insights:¶

Creating Networks¶

Observations:¶

Filtering Graphs¶

MST - Minimum Spanning Tree¶

Converted the correlation coefficient into a distance¶

Apply MST using the Kruskal Algorithm with NetworkX library:¶

Plot the MST Based Network Graph¶

Observations:¶

Computing Graph Statistics over Time creating a line plot¶

Plot the Average Shortest Path Length time line-plot¶

Stock Market Network Analysis and Visualization¶

Lets Calculate the log returns and compute the correlation matrix¶

Lets ransforms it into a distance matrix.¶

Apply the Minimum Spanning Tree (MST)¶

Plotting of the MST graph for the S&P500 stock market from 2010 to 2023¶

Observations and Insights:¶

Analyzing the network's topology with Centrality Measures¶

Apply Degree centrality¶

Observations and insights:¶

Apply Closeness centrality¶

Observations and insights:¶

Apply Betweenness centrality¶

Observations and insights:¶

Apply Eigenvector centrality¶

Observations and insights:¶

Conclusion:¶

Centrality and Distance-Based Analysis of the Network¶

Distance-Based Criteria¶

Distance on Degree Criterion¶

Distance on Correlation Criterion¶

Distance on Distance Criterion¶

Store the Results in a DataFrame¶

Add Closeness and Eigenvector Centrality to the DataFrame¶

Normalize and combine centrality scores¶

Weighted Scoring and Ranking of Stocks using Centrality and Distance-Based Metrics¶

Network Visualization of Central and Peripheral Stocks (2010-2023)¶

Observations:¶

Now lets simulate the performance of our Central and Peripheral portfolios against new historical data of the year 2024 for the S&P 500.¶

Upload the historic data of S&P500 Stocks from 02-01-2024 till 22-08-2024¶

Visualise the Data¶

Fetching S&P 500 Index Data¶

Observations:¶

Data Cleaning and Alignment¶

Visualise the Data¶

Calculating the Portfolios Values¶

Central and Peripheral Portfolios Values Calculation¶

S&P 500 Index Data value over time¶

Combine the portfolio values into a single DataFrame¶

Preview of the last few rows of the created single DataFrame¶

Portfolio Performance Comparison¶

Observations and Insights¶

Let's Work Together:¶